IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v396y2021ics0096300320308201.html
   My bibliography  Save this article

The convergence and stability of full discretization scheme for stochastic age-structured population models

Author

Listed:
  • Shi, Chunmei

Abstract

In this paper, a fully discretization scheme based on the implicit Euler method (IM) is considered for stochastic age-structured population models. The preservation of the total population with a suitable numerical boundary condition according to the biological meanings are shown. An explicit formula of the numerical basic reproductive number Rh is proposed by the technique that the numerical process is embedded into an l1(R)-valued integrable stochastic process with infinite stochastic Leslie operators. Furthermore, the convergence and connection between Rh and the stability of numerical solution is analyzed. The preservation and detection of the analytic stability through the numerical solutions are discussed for small stepsize. Finally, some numerical experiments including an infection-age model for modified SARS epidemic illustrate the verification and efficiency of our analysis.

Suggested Citation

  • Shi, Chunmei, 2021. "The convergence and stability of full discretization scheme for stochastic age-structured population models," Applied Mathematics and Computation, Elsevier, vol. 396(C).
    • Handle: RePEc:eee:apmaco:v:396:y:2021:i:c:s0096300320308201
    DOI: 10.1016/j.amc.2020.125867
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300320308201
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2020.125867?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Tan, Jianguo & Men, Weiwei & Pei, Yongzhen & Guo, Yongfeng, 2017. "Construction of positivity preserving numerical method for stochastic age-dependent population equations," Applied Mathematics and Computation, Elsevier, vol. 293(C), pages 57-64.
    2. Ma, Weijun & Ding, Baocang & Zhang, Qimin, 2015. "The existence and asymptotic behaviour of energy solutions to stochastic age-dependent population equations driven by Levy processes," Applied Mathematics and Computation, Elsevier, vol. 256(C), pages 656-665.
    3. Pei, Yongzhen & Yang, Hongfu & Zhang, Qimin & Shen, Fangfang, 2018. "Asymptotic mean-square boundedness of the numerical solutions of stochastic age-dependent population equations with Poisson jumps," Applied Mathematics and Computation, Elsevier, vol. 320(C), pages 524-534.
    4. Tan, Jianguo & Rathinasamy, A. & Pei, Yongzhen, 2015. "Convergence of the split-step θ-method for stochastic age-dependent population equations with Poisson jumps," Applied Mathematics and Computation, Elsevier, vol. 254(C), pages 305-317.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Tan, Jianguo & Chen, Yang & Men, Weiwei & Guo, Yongfeng, 2021. "Positivity and convergence of the balanced implicit method for the nonlinear jump-extended CIR model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 182(C), pages 195-210.
    2. Kang, Ting & Li, Qiang & Zhang, Qimin, 2019. "Numerical analysis of the balanced implicit method for stochastic age-dependent capital system with poisson jumps," Applied Mathematics and Computation, Elsevier, vol. 353(C), pages 166-177.
    3. Pei, Yongzhen & Yang, Hongfu & Zhang, Qimin & Shen, Fangfang, 2018. "Asymptotic mean-square boundedness of the numerical solutions of stochastic age-dependent population equations with Poisson jumps," Applied Mathematics and Computation, Elsevier, vol. 320(C), pages 524-534.
    4. Li, Yan & Zhang, Qimin, 2020. "The balanced implicit method of preserving positivity for the stochastic SIQS epidemic model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 538(C).
    5. Liu, Lidan & Meng, Xinzhu & Zhang, Tonghua, 2017. "Optimal control strategy for an impulsive stochastic competition system with time delays and jumps," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 477(C), pages 99-113.
    6. Ponosov, Arcady & Idels, Lev & Kadiev, Ramazan, 2020. "Stochastic McKendrick–Von Foerster models with applications," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 537(C).
    7. Zhang, Mengqing & Zhang, Qimin, 2019. "A positivity preserving numerical method for stochastic R&D model," Applied Mathematics and Computation, Elsevier, vol. 351(C), pages 193-203.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:apmaco:v:396:y:2021:i:c:s0096300320308201. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.